What are the odds of waiting 1325 hands for....
 

To all you statisticians out there, please provide the answer and explain how to calculate it. Starting a new database in PokerTracker, I noticed that after 1325 hands I had 168/169 unique hands. The hand I was missing was AA of course. Anyway, I finally got it after ~1330 hands (after all that wait it lost). So what are the odds this happening?

Thanks in advance!


The Greedy Gecko
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Re: What are the odds of waiting 1325 hands for....
 

0.24% - the math isn't that hard, the odds of being dealt AA is 1/221, so the odds of not being dealt AA is 220/221. The odds of this happening 1330 times in a row are:

(220/221)^1330

Re: What are the odds of waiting 1325 hands for....
 

BINOMDIST(0,1330,1/221,FALSE) = .24%

or simply

(220/221)^1330

Re: What are the odds of waiting 1325 hands for....
 

The other posters have answered the question "what are the odds of going 1325 hands without seeing AA?" -- which I don't think is the question you actually intended to ask.

I think what you were asking is, how long is it supposed to take before you see each of the 169 hands at least once each.

You have, in fact, gotten somewhat lucky. A quick simulation shows it takes an average of about 1640 tries to get all 169 possible hands. After 1325 tries, you can expect to have seen about 167.6 hands.

I seem to recall someone posting some Mathematica code a few weeks ago that gave an exact answer for how long it took to get all 169 hand types.

Re: What are the odds of waiting 1325 hands for....
 

A couple weeks ago I went 1700 hands and saw AA one time and it was WAY early in the day. Crazy but I'll see a longer streak eventually.

Re: What are the odds of waiting 1325 hands for....
 

Thank you all for the reply. Appreciate the info!

Re: What are the odds of waiting 1325 hands for....
 

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I seem to recall someone posting some Mathematica code a few weeks ago that gave an exact answer for how long it took to get all 169 hand types.

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